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ADSORPTION ISOTHERM
•Adsorption is a process that occurs when a gas or liquid solute accumulates on the surface of a solid or a liquid (adsorbent), forming a molecular or atomic film (adsorbate).•It is different from absorption, in which a substance diffuses into a liquid or solid to form a solution.•Adsorbent (also called substrate) - The solid that provides surface for adsorption.• Adsorbate - The gas or liquid substances which are to be adsorbed on Substrate.
ADSORBATE
ADSORBENT
Adsorption
ADSORPTION
1. It is mainly surface phenomenon. Surface concentration of adsorbed material is very high as compared to bulk. In fact, the bulk has practically no adsorbed material
2. A distinct chemical reaction occurs specially in chemisorption.
3. Some reactions is usually the result.
4. Only limited quantities of material are absorbed. It reaches saturation very easily.
5. For example, Ammonia is absorbed by charcoal.
ABSORPTION
1. The solid or liquid absorbs the gaseous or liquid matter. Concentration of the material is uniform throughout the absorbing material.
2. No chemical reaction is involved between the absorbed material and solid .
3. The absorbed material is recovered unchanged, as in case for the absorbent
4. Considerable amounts of absorbed material is ingested.
5. For example, ammonia is absorbed in water.
ADSORBENT
ABSORBATEADSORBATE
ABSORBENT
Physisorption Chemisorption
Force vanderWaal chemical bond
Number of adsorbed layers Multilayers Monolayer
Adsorption heat low (10-40 kJ/mol) high ( > 40 kJ/mol)
Temperature to occur low high
Selectivity low high
Physisorption Chemisorption
Equilibrium Rapidly Slowly
Nature Reversible Irreversible
Depends on Adsorbent Adsorbent and Adsorbate
Pressure Increases Decreases
Example Hydrogen adsorbed on charcoal
Hydrogen adsorbed on nickel
Adsorption On Solid SurfaceCharacterisation of adsorption system
Adsorption isotherm - most commonly used, especially to catalytic reaction system, T=const. The amount of adsorption as a function of pressure at set temperature
Adsorption isobar - (usage related to industrial applications)The amount of adsorption as a function of temperature at set pressure
Adsorption Isostere - (usage related to industrial applications)Adsorption pressure as a function of temperature at set volume
Pressure
Vol.
adso
rbed T1
T2 >T1T3 >T2
T4 >T3T5 >T4
Vol.
adso
rbed
Temperature
P1
P2>P1
P3>P2P4>P3
Pres
sure
Temperature
V2>V1
V1
V3>V2
V4>V3
Adsorption Isotherm Adsorption Isobar Adsorption Isostere
ISOTHERM ADSORPTION CURVE EXAMPLES
Type I Adsorption of O₂ and N₂ on charcoal at low temperatures viz.,78K
Type II Adsorption of N₂ on silica gel at 78K
Type III Adsorption of Br₂ on silica gel at 194k
Type IV Adsorption of C₆H₆ on Fe₂O₃ gel at 194K
Type V Adsorption of water vapours on charcoal at 373K
Amou
nt a
bsor
bed
Amou
nt a
bsor
bed
Amou
nt a
bsor
bed
Amou
nt a
bsor
bed
Amou
nt a
bsor
bed
P
P
P
P
P
TYPE OF ADSORPTION NATURE OF ADSORBENT
Langmuir type is found for porous materials with small pores e.g. charcoal
Sigmoid type for non-porous materials
Hyperbolic type porous materials with cohesive force between adsorbate molecules greater than the adhesive force between adsorbate molecules and adsorbent
Sharp approach to the line p₀ staged adsorption (first monolayer then build up of additional layers
Elongated S-type porous materials with cohesive force between adsorbate molecules and adsorbent being greater than that between adsorbate molecules
Langmuir isotherm
Basic assumptions
surface uniform monolayer adsorptionno interaction between adsorbed molecules and adsorbed molecules immobileAdsorbed molecule and desorbed molecule exist in equilibrium, as well as exhibit ideal gas behaviour
An schematic showing equivalent sites, occupied(blue) and unoccupied(red) clarifying the basic assumptions used in the model. The adsorption sites(heavy dots) are equivalent and can have unit occupancy. Also, the adsorbates are immobile on the surface
Case I - single molecule adsorption when adsorption is in a dynamic equilibrium
A(g) + M(surface site) D AMthe rate of adsorption rads = kads (1-q) P the rate of desorption rdes = kdes q
at equilibrium rads = rdes Þ kads (1-q) P = kdes q
rearrange it for q
let Þ B0 is adsorption coefficientq
CC
B PB P
s 0
01des
ads
kkB 0
PkkPkk
desads
desads
)/(1)/(
q
case I
A
A-B(g) + M(surface site) D A-M-Bthe rate of A-B adsorption rads=kads (1-qA )(1-qB)PAB=kads (1-q )2PAB
the rate of A-B desorption rdes=kdesqAqB =kdesq 2
at equilibrium rads = rdes Þ kads (1-q )2PAB= kdesq2
rearrange it for q
Let. Þ 1/20
1/20
)(1)(
AB
ABs
PBPB
CC
qdes
ads
kkB 0
)(1
)(
ABdesads
ABdesads
Pk/kPk/k
q
q=qA=qB
case II
A BBA
Case II - single molecule adsorbed dissociatively on one site
Case III - two molecules adsorbed on two sites
A(g) + B(g) + 2M(surface site) D A-M + B-M
the rate of A adsorption rads,A = kads,A (1- qA- qB) PA
the rate of B adsorption rads,B = kads,B (1- qA- qB) PB
the rate of A desorption rdes,A = kdes,A qA
the rate of B desorption rdes,B = kdes,B qB
at equilibrium rads ,A = rdes ,A and Þ rads ,B = rdes ,B
Þ kads,A(1-qA-qB)PA=kdes,AqA and kads,B(1-qA-qB)PB=kdes,BqB
rearrange it for q
where are adsorption coefficients of A & B.B,des
B,adsB,
A,des
A,adsA, k
kB
kk
B 00 and
BB,AA,
BB,B,sB
BB,AA,
AA,A,sA PBPB
PBCC
PBPBPB
CC
00
0
00
0
1
1
case III
A B
The Langmuir adsorption isotherm (cont’d)
B,des
B,adsB,
A,des
A,adsA, k
kB
kk
B 00 and
BB,AA,
BB,B,sB
BB,AA,
AA,A,sA
PBPBPB
CC
PBPBPB
CC
00
0
00
0
1
1
q
q
Adsorption
Strong kads>> kdes kads>> kdes
B0>>1 B0>>1
Weak kads<< kdes kads<< kdes
B0<<1 B0<<1
1/20
1/20
)(1)(
AB
ABs
PBPB
CC
q
des
ads
kkB 0
case II
A B
q
CC
B PB P
s 0
01
des
ads
kkB 0
case I
A
AdsorptionA, B both strong
A strong, B weak
A weak, B weak
BBAA
BBBsB
BBAA
AAAsA
PBPBPB
CC
PBPBPB
CC
,0,0
,0,
,0,0
,0,
q
q
BB,B,sB
AA,A,sA
PBC/CPBC/C
0
0
A
BA,B,B,sB
A,sA
PPB/BC/C
C/C
)(
1
00
q
q
case III
A B
1C
Csq 1C
Csq
PBCCs
0
q 1/20 )( PB
CCs
q
Langmuir adsorption isotherm
Langmuir adsorption isotherm established a logic picture of adsorption process It fits many adsorption systems but not at all The assumptions made by Langmuir do not hold in all situation, that causing error
Solid surface is heterogeneous thus the heat of adsorption is not a constant at different q Physisorption of gas molecules on a solid surface can be more than one layer
BB,AA,
BB,B,sB
BB,AA,
AA,A,sA
PBPBPB
CC
PBPBPB
CC
00
0
00
0
1
1
q
q
1/20
1/20
)(1)(
AB
ABs
PBPB
CC
q
q
CC
B PB P
s 0
01
large B0 (strong adsorp.)
small B0 (weak adsorp.)moderate B0Am
ount
ads
orbe
d
mono-layer
1C
Csq
PBCCs
0
q
Strong adsorption kads>> kdes
Weak adsorption kads<< kdes
case I
case II
Case III
Pressure
Disadvantages of the langmuir’s model
The Langmuir adsorption model deviates significantly in many cases, primarily because it fails to account for the surface roughness of the adsorbate. Rough inhomogeneous surfaces have multiple site-types available for adsorption, and some parameters vary from site to site, such as the heat of adsorption.The model also ignores adsorbate/adsorbate interactions. Experimentally, there is clear evidence for adsorbate/adsorbate interactions in heat of adsorption data. There are two kinds of adsorbate/adsorbate interactions: Direct interaction and Indirect interaction1. Direct interactions are between adjacent adsorbed molecules, which could make adsorbing
near another adsorbate molecule more or less favorable and greatly affects high-coverage behavior.
2. In indirect interactions, the adsorbate changes the surface around the adsorbed site, which in turn affects the adsorption of other adsorbate molecules nearby.
The Temkin (or Slygin-Frumkin) isotherm This isotherm takes into accounts of indirect adsorbate-adsorbate interactions on
adsorption isotherms. Temkin noted experimentally that heats of adsorption would more often decrease than increase with increasing coverage.From ads-des equilibrium, ads. rate º des. rate rads= kads(1-q)P º rdes= kdesq
where Qs is the heat of adsorption. When Qs is a linear function of qi. Qs=Q0-iS (Q0 is a constant, i is the number and S represents the surface site),
the overall coverage
When b1P >>1 and b1Pexp(-i/RT) <<1, we have q =c1ln(c2P), where c1 & c2 are constants
Valid for some adsorption systems.
DH o
f ads
q
LangmuirTemkin
BET (Brunauer-Emmett-Teller) isotherm
– Many physical adsorption isotherms were found, such as the types II and III, that the adsorption does not complete the first layer (monolayer) before it continues to stack on the subsequent layer (thus the S-shape of types II and III isotherms
ADSORBENT
ADSORBATE
Postulates of B.E.T Equation• This equation is an extension of the interpretation, of the monomolecular layer
adsorption.• The derivation is based on the same kinetic picture and the assumption that the
condensation force are the principle force or the main force in adsorption.• As in Langmuir’s adsorption theory, the rate of evaporation from the first layer is
equal to rate of condensation on each bare or uncovered surface.• Additionally, the rate of the evaporation from each succeeding layer is equal to rate
of condensation on the preceding layer.• The heat of adsorption is exponentially involved in each of the equilibrium
evaporation rate expression.• The heat of adsorption in each layer other than the first is equal to the heat of
liquefaction of the bulk adsorbate material.
Rate of condensation On bare surface
Rate of evapoarion from first layer
Derivation of B.E.T. equation• The derivation can be carried out by various steps on basis of the postulates.
S₃ S₁S₂ S₁ S₂
Let S₀, S₁, S₂, ……….Si represent the surface area of the adsorbent which is covered by 0,1,2,..........i layers of the adsorbed molecules.
Since at equilibrium S₀ remains constant, the rate of evaporation from the first layer is equal to rate of condensation on each bare or uncovered surface.
Rate of condensation is directly proportional to pressure of gas, i.e., pS₀,S₀, Rate of condensation on bare surface = a₁pS₀ ,where a₁ is a constant
Rate of evaporation is propotional to the surface which is covered, i.e., k₁S₁. Rate of evaporation from first layer= b₁S₁ e-E1/RT
Therefore, a₁pS₀ = b₁S₁ e-E1/RT …….(1)
At equilibrium, S₁ must also remains constant. S₁ can change in four different ways:i. By condensation on the bare surfaceii. By evaporation from first layeriii. By condensation on the first layeriv. By evaporation from the second layer
S₃ S₁S₂ S₁ S₂S₀
a₂pS₁ + b₁S₁ e-E1/RT = a₁pS₀+ b₂S₂ e-E2/RT
from equation (1) we have, a₂pS₁ = b₂S₂ e-E2/RT ……(2)
where a₂, b₂ and E₂ have their usual significance.ion the rate of condensation on the top of the first layer is equal to the rate of evaporation
from the the second layer. a₃pS₂ = b₃S₃ e-E3/RT
…. …. …. …. …. …. …. ….…. …. …. ….
aipSi-1 = biSi e-Ei/RT …….(3)Total surface area of the catalyst (A) is
...…. (4)
Total volume adsorbed is given by
……(5)
Where vₐ= vₒA = volume of the gas adsorbed when the entire adsorbent is covered with complete unimolecular layer
The summation of equation (6) can be carried out if we make the simplifying equation as that,(i) E₂=E₃=E₄=………………………..=Eᵢ=El
where El =heat of liquefaction.(ii)
=g,
Where g = appropriate constantWe can express S₁, S₂, S₃…….Sᵢ in terms of Sₒ as follows:
Where
[From 2]
Where
[From 7]Similarly, ..........(8)
................ ................
or
WHERENow equation (6) can be written as ,
............(9)
The summation represented in the numerator and denominator is merely the sum of an infinite geometrical progressions (G.P) we also have that,
So , equation 9 reduce to
Equation (10) is known as B.E.T. equation
Comment on the BET isotherm BET equation fits reasonably well all known adsorption isotherms observed so
far (types I to V) for various types of solid, although there is fundamental defect in the theory because of the assumptions made (no interaction between adsorbed molecules, surface homogeneity and liquefaction heat for all subsequent layers being equal).
BET isotherm, as well as all other isotherms, gives accurate account of adsorption isotherm only within restricted pressure range. At very low (P/P0<0.05) and high relative pressure (P/P0>0.35) it becomes less applicable.
The most significant contribution of BET isotherm to the surface science is that the theory provided the first applicable means of accurate determination of the surface area of a solid (since in 1945).
Many new development in relation to the theory of adsorption isotherm, most of them are accurate for a specific system under specific conditions.
Freundlich Adsorption Isotherm•The Freundlich isotherm is the most important multisite adsorption isotherm for rough surfaces.•The freundlich equation or freundlich adsorption isotherm , is a curve relating the concentration of a solute on the surface of adsorbent to the concentration of the solute in a liquid with which it is in contact.• In 1909.freundlich gave an empirical expression representing the isothermal variation of adsorption of a quantity of gas adsorbed by unit mass of solid adsorbent with pressure. This equation is known as FREUNDLICH ADSORPTION ISOTHERM
x m = k P ⅟n ̸
Where x is the mass of the gas adsorbed on mass m of the adsorbent at pressure p and k, n are constants whose values depend upon adsorbent and
gas at particular temperature.
Explanation of Freundlich Adsorption equation
At low pressure, extent of adsorption is directly proportional to pressure (raised to power one). x m ∞ P' ̸ At high pressure, extent of adsorption is independent of pressure (raised to power zero). x m ∞ P° ̸ Therefore at intermediate value of pressure, adsorption is directly proportional to pressure
raised to power 1/n .Here n is a variable whose value is greater than one. therefore, x m ∞ k P ⅟n ̸Using constant of proportionality, k, also known as adsorption constant we get x m = k P ⅟n ̸The above equation is known as Freundlich adsorption equation.
Plotting of Freundlich Adsorption Isotherm
As per Freundlich adsorption equation x m = k P ⅟n ̸Taking log both sides of equation, we get, log {x m} = logk + ⅟n logp ̸
The equation above equation is comparable with comparable with equation of straight line, y = m x + c where, m represents slope of the line and c represents intercept on y axis.
Plotting a graph between log(x/m) and log p, we will get a straight line with value of slope equal to 1/n and log k as y-axis intercept.
It has limited applicability. It can be applied to study adsorption from solutions.
Fundamental Difference between Langmuir and Freundlich
▪ Langmuir’s model was a theoretical construct, while the Freundlich isotherm is empirical.▪ In the Langmuir model, it is assumed that at a maximum coverage there is only a monomolecular layer on the surface. This means that there is no stacking of adsorbed molecules. The Freundlich isotherm does not have the restriction.
LIMITATION OF FREUNDLCH ADSORPTION EQUATION
• Experimently it was determined that extent of adsorption varies directly with presssure till saturation pressure is reached. Beyond that point rate of adsorption saturates even after applying higher pressure .
• Thus, Freundlich adsorption equation failed at higher pressure.
Name Isotherm equation Application Note
Langmuir Chemisorption andphysisorption
Useful in analysis of reaction mechanism
Temkin q =c1ln(c2P) Chemisorption Chemisorption
Freundlich Chemisorption andphysisorption
Easy to fit adsorption data
BET Multilayer physisorption Useful in surface area determination
Summary of adsorption isotherms
q
CC
B PB P
s 0
01
211
C/pcq
)/(11)/1(
/0
0
0 PPcVc
cVPPVPP
mm
-
-
